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Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating projections between the nonnegative orthant and the set of low-rank tensors, using STHOSVD and TTSVD…

Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…

Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Diffusion magnetic resonance imaging (dMRI) data allow to reconstruct the 3D pathways of axons within the white matter of the brain as a tractography. The analysis of tractographies has drawn attention from the machine learning and pattern…

An increasing number of emerging applications in data science and engineering are based on multidimensional and structurally rich data. The irregularities, however, of high-dimensional data often compromise the effectiveness of standard…

Topo-Tomography (TT) is a synchrotron-based X-ray diffraction imaging technique used to characterize grain shape and crystal orientation in polycrystalline samples. This work aims to provide a decisive and fundamental understanding of 3D…

Transformer architecture has gained popularity due to its ability to scale with large dataset. Consequently, there is a need to reduce the model size and latency, especially for on-device deployment. We focus on vision transformer proposed…

Low-Rank Factorization (LRF) is a widely adopted technique for compressing deep neural networks (DNNs). However, it faces several challenges, including optimal rank selection, a vast design space, long fine-tuning times, and limited…

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…

Tractography has become an indispensable part of brain connectivity studies. However, it is currently facing problems with reliability. In particular, a substantial amount of nerve fiber reconstructions (streamlines) in tractograms produced…

Doctors and researchers routinely use diffusion tensor imaging (DTI) and tractography to visualize the fibrous structure of tissues in the human body. This paper explores the connection of these techniques to the painterly rendering of…

Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex…

Deep neural networks typically impose significant computational loads and memory consumption. Moreover, the large parameters pose constraints on deploying the model on edge devices such as embedded systems. Tensor decomposition offers a…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

In this paper a new Riemannian rank adaptive method (RRAM) is proposed for the low-rank tensor completion problem (LRTCP) formulated as a least-squares optimization problem on the algebraic variety of tensors of bounded tensor-train (TT)…

We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…

The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…